2024/03/28 by Y. Tsutsui, Tsutsui, Yuki
Computer Science · #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2403.19576
openalex publication_date 2024/03/28 · openalex created_date 2024/03/30 · openalex updated_date 2026/07/28
López de Medrano, Rincón and Shaw defined the Chern classes on tropical manifolds as an extension of their theory of the Chern-Schwartz-MacPherson cycles on matroids. This makes it possible to define the Riemann-Roch number of tropical Cartier divisors on compact tropical manifolds. In this paper, we introduce the notion of a moderate position, and discuss a conjecture that the Riemann-Roch number RR(X;D) of a tropical submanifold D of codimension 1 in moderate position on a compact tropical manifold X is equal to the topological Euler characteristic of the complement X∖ D. In particular, we prove it and its generalization when dim X=2 and X admits a Delzant face structure.